In animation and filmmaking, a key frame (or keyframe) is a drawing or shot that defines the starting and ending points of a smooth transition. These are called frames because their position in time is measured in frames on a strip of film or on a digital video editing timeline. A sequence of key frames defines which movement the viewer will see, whereas the position of the key frames on the film, video, or animation defines the timing of the movement. Because only two or three key frames over the span of a second do not create the illusion of movement, the remaining frames are filled with "inbetweens". == Use of key frames as a means to change parameters == In software packages that support animation, especially 3D graphics, there are many parameters that can be changed for any one object. One example of such an object is a light. In 3D graphics, lights function similarly to real-world lights. They cause illumination, cast shadows, and create specular highlights. Lights have many parameters, including light intensity, beam size, light color, and the texture cast by the light. Supposing that an animator wants the beam size to change smoothly from one value to another within a predefined period of time, that could be achieved by using key frames. At the start of the animation, a beam size value is set. Another value is set for the end of the animation. Thus, the software program automatically interpolates the two values, creating a smooth transition. == Video editing == In non-linear digital video editing, as well as in video compositing software, a key frame is a frame used to indicate the beginning or end of a change made to a parameter. For example, a key frame could be set to indicate the point at which audio will have faded up or down to a certain level. == Video compression == In video compression, a key frame, also known as an intra-frame, is a frame in which a complete image is stored in the data stream. In video compression, only changes that occur from one frame to the next are stored in the data stream, in order to greatly reduce the amount of information that must be stored. This technique capitalizes on the fact that most video sources (such as a typical movie) have only small changes in the image from one frame to the next. Whenever a drastic change to the image occurs, such as when switching from one camera shot to another or at a scene change, a key frame must be created. The entire image for the frame must be output when the visual difference between the two frames is so great that representing the new image incrementally from the previous frame would require more data than recreating the whole image. Because video compression only stores incremental changes between frames (except for key frames), it is not possible to fast-forward or rewind to any arbitrary spot in the video stream. That is because the data for a given frame only represents how that frame was different from the preceding one. For that reason, it is beneficial to include key frames at arbitrary intervals while encoding video. For example, a key frame may be output once for each 10 seconds of video, even though the video image does not change enough visually to warrant the automatic creation of the key frame. That would allow seeking within the video stream at a minimum of 10-second intervals. The downside is that the resulting video stream will be larger in disk size because many key frames are added when they are not necessary for the frame's visual representation. This drawback, however, does not produce significant compression loss when the bitrate is already set at a high value for better quality (as in the DVD MPEG-2 format).
Event store
An event store is a type of database optimized for storage of events. Conceptually, an event store records only the events affecting an entity, dossier, or policy, and the state of the entity at any point in its history can be reconstructed by replaying its contributing events in sequential order. Events (and their corresponding data) are the only "real" facts that should be stored in the database. All other objects can be derived from these events, meaning they are instantiated in memory by runtime code as needed (e.g. for showing in a user interface). In theory, any object that aggregates over recorded event data is not stored in the database. Instead these objects are built 'on the fly', by traversing the event history. When the aggregated object instance is no longer needed, it can simply be discarded (released from memory). == Example with insurance policies == For example, the event store concept of a database can be applied to insurance policies or pension dossiers. In these policies or dossiers the instantiation of each object that make up the dossier or policy (the person, partner(s), employments, etc.) can be derived and can be instantiated in memory based on the real world events. == Double timeline == A crucial part of an event store database is that each event has a double timeline: This enables event stores to correct errors of events that have been entered into the event store database before. The two dates are: Valid date is the date at which the event has become valid. Transaction date is the date at which the event is entered into the database. == Error correction == Another crucial part of an event store database is that events that are stored are not allowed to be changed. Once stored, also erroneous events are not changed anymore. The only way to change (or better: correct) these events is to instantiate a new event with the new values and using the double timeline. A correcting event would have the new values of the original event, with an event data of that corrected event, but a different transaction date. This mechanism ensures reproducibility at each moment in the time, even in the time period before the correction has taken place. It also allows to reproduce situations based on erroneous events (if required). == Advantages and disadvantages == One advantage of the event store concept is that handling the effects of back dated events (events that take effect before previous events and that may even invalidate them) is much easier. An event store will simplify the code in that rolling back erroneous situations and rolling up the new, correct situations is not needed anymore. Disadvantage may be that the code needs to re-instantiate all objects in memory based on the events each time a service call is received for a specific dossier or policy. == Compared to regular databases == In regular databases, handling backdated events to correct previous, erroneous events can be painful as it often results in rolling back all previous, erroneous transactions and objects and rolling up the new, correct transactions and objects. In an event store, only the new event (and its corresponding facts) are stored. The code will then redetermine the transactions and objects based on the new facts in memory.
The Machine Question
The Machine Question: Critical Perspectives on AI, Robots, and Ethics is a 2012 nonfiction book by David J. Gunkel that discusses the evolution of the theory of human ethical responsibilities toward non-human things and to what extent intelligent, autonomous machines can be considered to have legitimate moral responsibilities and what legitimate claims to moral consideration they can hold. The book was awarded as the 2012 Best Single Authored Book by the Communication Ethics Division of the National Communication Association. == Content == The book is spread across three chapters, with the first two chapters focusing on an overall review of the history of philosophy and its discussion of moral agency, moral rights, human rights, and animal rights and the third chapter focusing on what defines "thingness" and why machines have been excluded from moral and ethical consideration due to a misuse of the patient/agent binary. The first chapter, titled Moral Agency, breaks down the history of said agency based on what it included and excluded in various parts of history. Gunkel also raises the conflict between discussing the morality of humans toward objects and the theory of the philosophy of technology that "technology is merely a tool: a means to an end". The main issue, he explains, in defining what constitutes an appropriate moral agent is that there will be things left outside of what is included, as the definition is based on a set of characteristics that will inherently not be all-encompassing. The subject of consciousness is broached and subsequently derided by Gunkel because of it being one of the main arguments against machine rights, while Gunkel points out that no "settled definition" of the term exists and that he considers it no better than a synonym used for "the occultish soul". In addition, the issue of the other minds problem entails that no proper understanding of consciousness can come to pass due to the inability to properly understand the mind of a being that is not oneself. The second chapter, titled Moral Patiency, focuses on the patient end of the topic and discusses the expansion of the fields of animal studies and environmental studies. Gunkel describes moral patients as the ones that are to be the object of moral consideration and deserve such consideration even if they lack their own agency, such as animals, thus allowing moral consideration itself to be broader and more inclusive. The topic of other minds is discussed again when examining the question of whether animals can suffer, a question that Gunkel ultimately abandons because it encounters the same problems that the topic of consciousness does. Especially because the subject of animal rights is often only afforded for the animals deemed to be "cute", but often not including "reptiles, insects, or microbes". Gunkel continues on to examine environmental ethics and information ethics, but finds them to be too anthropocentric, just as all the other examined models have been. The third chapter, titled Thinking Otherwise, proposes a combination of Heideggerian ontology and Levinasian ethics to properly discuss the otherness of technology and machines, but finds that the patient/agent binary is unable to be properly extended to confine the extent of "the machine question". In discussing the land ethic philosophy espoused by Aldo Leopold, Gunkel proposes that it is the entire relationship between agent and patient that should have moral consideration and not a specific definition based on either side, as each part contributes to the relationship as a whole and cannot be removed without breaking that relationship. == Critical reception == Choice: Current Reviews for Academic Libraries writer R. S. Stansbury explained that the book is able to use simple examples to discuss difficult topics and separate ideas and that it would be "useful for philosophy students, and for engineering students interested in exploring the ethical implications of their work". Dominika Dzwonkowska, writing for International Philosophical Quarterly, stated that the "unprecedented value of the book is that Gunkel not only analyzes important aspects of the immediate problem but also that he places his discussion in the context of philosophical discussions on such related issues as rights discourse." Mark Coeckelbergh in Ethics and Information Technology noted that focusing on the question itself of the machine question allows further exploration of machine ethics and the expansion of general ethics and that the book's questions point out that "good, critical philosophical reflection on machines is not only about how we should cope with machines, but also about how we (should) think and what role technology plays (and should play) in this thinking." A review in Notre Dame Philosophical Reviews by Colin Allen criticized some of Gunkel's methodology and the indecisiveness of his ultimate answer to the machine question, but also acknowledged that the book "succeeded in connecting the ethics of robots and AI to a much broader ethical discussion than has been represented in the literature on machine ethics to date". Blay Whitby, in a review for AISB Quarterly, lauded The Machine Question for its "clear exposition" and wide range of references to other works, concluding that the book is "essential reading for philosophers interested in AI, robot ethics, or animal ethics". In a twin review of The Machine Question and Robot Ethics: The Ethical and Social Implications of Robots by Patrick Lin, Keith Abney, and George A. Bekey, Techné: Research in Philosophy and Technology reviewer Jeff Shaw called Gunkel's book a good introduction to the "complex field of robot ethics" and that both books are "highly recommended to both the general reader as well as to experts in the field of robotics, philosophy, and ethics." In a 2017 paper for Ethics and Information Technology, Katharyn Hogan investigated whether the machine question presented by Gunkel in the book is any different from the longstanding animal question. She concludes that the real question that is revealed from this discussion is whether humans deserve any moral preference over artificial life in the first place.
Texas Senate Bill 20
Texas Senate Bill 20 (S.B. 20), also known as the "Stopping AI-Generated Child Pornography Act", is a 2025 law in the state of Texas that creates new criminal offenses for those who possess, promote, or view visual material deemed obscene, which is said to depict a child, whether it is an actual person, animated or cartoon depiction, or an image of someone created through computer software or artificial intelligence. It was passed by the Texas Legislature on May 28, 2025, unanimously in both chambers. It was signed into law by Governor Greg Abbott on June 20, 2025. It went into effect on September 1, 2025. It was authored by Pete Flores and co-sponsored by Brent Hagenbuch, Juan Hinojosa, Joan Huffman, Phil King, and Tan Parker, as part of a package of legislation in the Texas House and Senate about A.I. and child pornography. Some supporters called it "common-sense" legislation falling within the "proper role" of government, protecting children and the "common good" within the state, with Heidi Ruiz, a police sergeant in Houston, describing the bill as "fantastic" and "fabulous." The bill drew comparisons to language, within Texas state legislation, which aimed to institute state-level book bans. Critics described the law as unconstitutional, saying it violated the Free Speech Clause of the First Amendment which prohibits abridgement of freedom of speech and the press, including the legal precedent set in Ashcroft v. Free Speech Coalition. The Comic Book Legal Defense Fund vowed to support those wrongly accused under the law. Much of the controversy regarding S.B. 20 involves the broad language pertaining to "obscene" pornographic images as including A.I.-created, animated, and cartoon depictions, with some critics arguing it could have a chilling effect on anime, manga, graphic novels, and other media produced, distributed, or created within Texas. == Provisions == S.B. 20 gives Texas police more provisions to restrict artificial intelligence-created child pornography, creating new criminal charge for possessing material depicting an underage person, under age 18, whether this child is an actual person or not. Those charged with this felony offense could go to state jail, but this could be elevated if the person charged has a prior conviction, of a $10,000 fine and two years in prison. == Reactions == === Support === Lieutenant Governor Dan Patrick applauded the unanimous passage of the law in the Texas Senate and called it "a priority" to protect children in Texas, and Texas citizens and thanked Pete Flores for his work on "this important issue". He later described the bill as part of the "bold, conservative agenda" that the Texas legislature passed during the 2025 legislative session. Phil King, one of the bill's co-sponsors, said that issue of child pornography had "infiltrated" the state's schools and said he was proud that the Texas legislature had "taken decisive action to protect our vulnerable Texans". Another co-sponsor of the legislation, Tan Parker described the law as "decisive action" to protect the children within Texas, and said he looked "forward to advancing this critical legislation" onward from the Texas Senate Criminal Justice Committee. He also described the legislation as "critical" action to protect the state's children from A.I.-generated child pornography and an "effective tool for law enforcement" to crack down on child porn perpetrators. Other supporters, such as police, and prosecutors, called the legislation an "important step" to ensure that images generated with A.I., along with deepfakes, "can't be shared with impunity" and necessary to ensure children's protection. Flores told senators that technology which enabled the production of "offensive" material by child predators had "no redeeming value whatsoever" and asserted that the materials had often been "used to groom and abuse children". John Leigh, a co-founder of Anime Matsuri, one of the largest conventions for anime within Texas, reassured those who contacted him, saying that the law is not targeted at anime and manga fans, stated that he supported the legislation, describing it as a step "in the right direction," and said that he did not believe it would "negatively impact" anime or related art in the state. Also, State Representative Dade Phelan emphasized the legislation's urgency to deal with A.I. and child pornography, adding that they need to "put some guardrails on it to where the public is being taken care of". The Texas Policy Research Foundation supported the legislation, saying that although it may lead to increased demands on state and local governmental resources, higher costs for local governments, and possible "civil liberty concerns" around online censorship, it represents a "necessary legal update" to address exploitation of children online, while "modernizing enforcement mechanisms" and recommended that lawmakers vote in favor of the law. Additionally, the group Texans for Fiscal Responsibility supported the law, arguing that it strengthened state law, upheld public safety, protected minors, and called it a "common-sense bill" protecting and promoting the "common good", children, and fell within the "proper role" of government. The Texas Public Policy Foundation also expressed their support for the law. A policy director for aforementioned conservative think tank, Zach Whiting, told the Texas Senate Committee on Criminal Justice, on March 4, 2025, that the foundation would assist legislators ans staff to "advance any and all measures to protect kids online" and shared an excerpt from of research paper about threats posed by A.I. in creating "sexually explicit deepfakes of children". === Opposition === Although the bill passed both chambers unanimously, there were some reports that the bill stalled due to opposition from Democratic lawmakers. Additionally, some individuals expressed concerns about the broad nature of the law's provisions. Anime Matsuri co-founder Deneice Leigh called for the law's wording to be clarified because "artists are anxious about displaying or selling fan art" even if the intention is "not be to penalize creators". She also described the bill as "vague and open to interpretation" as to what would be considered obscene and offensive while noting that the bill is not aiming to "target artists". Benjamin Napier, owner of Mansfield Comics and Manga in Mansfield, Texas, said that at first he felt the law was "ridiculous" and "kind of frivolous" at first, part of a "misguided puritanical onslaught", and noted that he would not cow "to the puritanical regime" if it was enacted. Kirsten Cather, an Asian Studies scholar at University of Texas, expressed concern at the law's misinterpretation because "many anime characters appear youthful, regardless of their actual age", said that the law could "stifle creative expression", and noted that the law's scope is broad enough to have manga and anime under scrutiny, a "real slippery slope here that's being breached". Marcel Green of Screen Rant said that the law's ambiguity led to concerns from manga and anime fans, and theorized that the law's application to a fan within Texas, who downloaded the 368th chapter of My Hero Academia, which has a "sexualized depiction" of an "underage high school student", would result in a criminal offense of "180 days to two years in state jail, along with a fine of up to $10,000". Green also said the law is problematic because many anime and manga characters are young, with many protagonists as minors and argued that the law could apply in limited cases, if state officials deemed an anime or manga under scrutiny as lacking "artistic value". Evan D. Mullicane, on the same site, said the vague wording of the legislation made it "dangerous" for anime such as Dragon Ball and Naruto, and could impact more than hentai, predicting it will be used against more than its "intended target" and be used to censor stories with "young LGBTQIA characters". Another critic on the same site, Carlyle Edmundson, called for anime fans to step up and prevent the law's enactment "for the good of artists and fans everywhere", saying that the legislation was "draconian" and claimed it was the most extreme case of anime and manga censorship in U.S. history. Nick Valdez of ComicBook.com said that the legislation could lead to censorship of "many anime and manga projects," like Kill la Kill and The 100 Girlfriends Who Really, Really, Really, Really, Really Love You, becoming a crime, and said that even if the law is enforced in a case-by-case basis, it could lead to a "much larger ban of materials in the state" itself due to the content of certain manga and anime. Vanessa Esguerra of The Mary Sue argued that possession of manga like Berserk and Vagabond, or viewing Dandadan, could be deemed illegal under the law, due to various parts of each of these media, and asserted that viewing and owning certain anime and other media, falling under the law's provisions,
Linear belief function
Linear belief functions are an extension of the Dempster–Shafer theory of belief functions to the case when variables of interest are continuous. Examples of such variables include financial asset prices, portfolio performance, and other antecedent and consequent variables. The theory was originally proposed by Arthur P. Dempster in the context of Kalman Filters and later was elaborated, refined, and applied to knowledge representation in artificial intelligence and decision making in finance and accounting by Liping Liu. == Concept == A linear belief function intends to represent our belief regarding the location of the true value as follows: We are certain that the truth is on a so-called certainty hyperplane but we do not know its exact location; along some dimensions of the certainty hyperplane, we believe the true value could be anywhere from –∞ to +∞ and the probability of being at a particular location is described by a normal distribution; along other dimensions, our knowledge is vacuous, i.e., the true value is somewhere from –∞ to +∞ but the associated probability is unknown. A belief function in general is defined by a mass function over a class of focal elements, which may have nonempty intersections. A linear belief function is a special type of belief function in the sense that its focal elements are exclusive, parallel sub-hyperplanes over the certainty hyperplane and its mass function is a normal distribution across the sub-hyperplanes. Based on the above geometrical description, Shafer and Liu propose two mathematical representations of a LBF: a wide-sense inner product and a linear functional in the variable space, and as their duals over a hyperplane in the sample space. Monney proposes still another structure called Gaussian hints. Although these representations are mathematically neat, they tend to be unsuitable for knowledge representation in expert systems. == Knowledge representation == A linear belief function can represent both logical and probabilistic knowledge for three types of variables: deterministic such as an observable or controllable, random whose distribution is normal, and vacuous on which no knowledge bears. Logical knowledge is represented by linear equations, or geometrically, a certainty hyperplane. Probabilistic knowledge is represented by a normal distribution across all parallel focal elements. In general, assume X is a vector of multiple normal variables with mean μ and covariance Σ. Then, the multivariate normal distribution can be equivalently represented as a moment matrix: M ( X ) = ( μ Σ ) . {\displaystyle M(X)=\left({\begin{array}{{20}c}\mu \\\Sigma \end{array}}\right).} If the distribution is non-degenerate, i.e., Σ has a full rank and its inverse exists, the moment matrix can be fully swept: M ( X → ) = ( μ Σ − 1 − Σ − 1 ) {\displaystyle M({\vec {X}})=\left({\begin{array}{{20}c}\mu \Sigma ^{-1}\\-\Sigma ^{-1}\end{array}}\right)} Except for normalization constant, the above equation completely determines the normal density function for X. Therefore, M ( X → ) {\displaystyle M({\vec {X}})} represents the probability distribution of X in the potential form. These two simple matrices allow us to represent three special cases of linear belief functions. First, for an ordinary normal probability distribution M(X) represents it. Second, suppose one makes a direct observation on X and obtains a value μ. In this case, since there is no uncertainty, both variance and covariance vanish, i.e., Σ = 0. Thus, a direct observation can be represented as: M ( X ) = ( μ 0 ) {\displaystyle M(X)=\left({\begin{array}{{20}c}\mu \\0\end{array}}\right)} Third, suppose one is completely ignorant about X. This is a very thorny case in Bayesian statistics since the density function does not exist. By using the fully swept moment matrix, we represent the vacuous linear belief functions as a zero matrix in the swept form follows: M ( X → ) = [ 0 0 ] {\displaystyle M({\vec {X}})=\left[{\begin{array}{{20}c}0\\0\end{array}}\right]} One way to understand the representation is to imagine complete ignorance as the limiting case when the variance of X approaches to ∞, where one can show that Σ−1 = 0 and hence M ( X → ) {\displaystyle M({\vec {X}})} vanishes. However, the above equation is not the same as an improper prior or normal distribution with infinite variance. In fact, it does not correspond to any unique probability distribution. For this reason, a better way is to understand the vacuous linear belief functions as the neutral element for combination (see later). To represent the remaining three special cases, we need the concept of partial sweeping. Unlike a full sweeping, a partial sweeping is a transformation on a subset of variables. Suppose X and Y are two vectors of normal variables with the joint moment matrix: M ( X , Y ) = [ μ 1 Σ 11 Σ 21 μ 2 Σ 12 Σ 22 ] {\displaystyle M(X,Y)=\left[{\begin{array}{{20}c}{\begin{array}{{20}c}\mu _{1}\\\Sigma _{11}\\\Sigma _{21}\end{array}}&{\begin{array}{{20}c}\mu _{2}\\\Sigma _{12}\\\Sigma _{22}\end{array}}\end{array}}\right]} Then M(X, Y) may be partially swept. For example, we can define the partial sweeping on X as follows: M ( X → , Y ) = [ μ 1 ( Σ 11 ) − 1 − ( Σ 11 ) − 1 Σ 21 ( Σ 11 ) − 1 μ 2 − μ 1 ( Σ 11 ) − 1 Σ 12 ( Σ 11 ) − 1 Σ 12 Σ 22 − Σ 21 ( Σ 11 ) − 1 Σ 12 ] {\displaystyle M({\vec {X}},Y)=\left[{\begin{array}{{20}c}{\begin{array}{{20}c}\mu _{1}(\Sigma _{11})^{-1}\\-(\Sigma _{11})^{-1}\\\Sigma _{21}(\Sigma _{11})^{-1}\end{array}}&{\begin{array}{{20}c}\mu _{2}-\mu _{1}(\Sigma _{11})^{-1}\Sigma _{12}\\(\Sigma _{11})^{-1}\Sigma _{12}\\\Sigma _{22}-\Sigma _{21}(\Sigma _{11})^{-1}\Sigma _{12}\end{array}}\end{array}}\right]} If X is one-dimensional, a partial sweeping replaces the variance of X by its negative inverse and multiplies the inverse with other elements. If X is multidimensional, the operation involves the inverse of the covariance matrix of X and other multiplications. A swept matrix obtained from a partial sweeping on a subset of variables can be equivalently obtained by a sequence of partial sweepings on each individual variable in the subset and the order of the sequence does not matter. Similarly, a fully swept matrix is the result of partial sweepings on all variables. We can make two observations. First, after the partial sweeping on X, the mean vector and covariance matrix of X are respectively μ 1 ( Σ 11 ) − 1 {\displaystyle \mu _{1}(\Sigma _{11})^{-1}} and − ( Σ 11 ) − 1 {\displaystyle -(\Sigma _{11})^{-1}} , which are the same as that of a full sweeping of the marginal moment matrix of X. Thus, the elements corresponding to X in the above partial sweeping equation represent the marginal distribution of X in potential form. Second, according to statistics, μ 2 − μ 1 ( Σ 11 ) − 1 Σ 12 {\displaystyle \mu _{2}-\mu _{1}(\Sigma _{11})^{-1}\Sigma _{12}} is the conditional mean of Y given X = 0; Σ 22 − Σ 21 ( Σ 11 ) − 1 Σ 12 {\displaystyle \Sigma _{22}-\Sigma _{21}(\Sigma _{11})^{-1}\Sigma _{12}} is the conditional covariance matrix of Y given X = 0; and ( Σ 11 ) − 1 Σ 12 {\displaystyle (\Sigma _{11})^{-1}\Sigma _{12}} is the slope of the regression model of Y on X. Therefore, the elements corresponding to Y indices and the intersection of X and Y in M ( X → , Y ) {\displaystyle M({\vec {X}},Y)} represents the conditional distribution of Y given X = 0. These semantics render the partial sweeping operation a useful method for manipulating multivariate normal distributions. They also form the basis of the moment matrix representations for the three remaining important cases of linear belief functions, including proper belief functions, linear equations, and linear regression models. === Proper linear belief functions === For variables X and Y, assume there exists a piece of evidence justifying a normal distribution for variables Y while bearing no opinions for variables X. Also, assume that X and Y are not perfectly linearly related, i.e., their correlation is less than 1. This case involves a mix of an ordinary normal distribution for Y and a vacuous belief function for X. Thus, we represent it using a partially swept matrix as follows: M ( X → , Y ) = [ 0 0 0 μ 2 0 Σ 22 ] {\displaystyle M({\vec {X}},Y)=\left[{\begin{array}{{20}c}{\begin{array}{{20}c}0\\0\\0\end{array}}&{\begin{array}{{20}c}\mu _{2}\\0\\\Sigma _{22}\\\end{array}}\end{array}}\right]} This is how we could understand the representation. Since we are ignorant on X, we use its swept form and set μ 1 ( Σ 11 ) − 1 = 0 {\displaystyle \mu _{1}(\Sigma _{11})^{-1}=0} and − ( Σ 11 ) − 1 = 0 {\displaystyle -(\Sigma _{11})^{-1}=0} . Since the correlation between X and Y is less than 1, the regression coefficient of X on Y approaches to 0 when the variance of X approaches to ∞. Therefore, ( Σ 11 ) − 1 Σ 12 = 0 {\displaystyle (\Sigma _{11})^{-1}\Sigma _{12}=0} . Similarly, one can prove that μ 1 ( Σ 11 ) − 1 Σ 12 = 0 {\displaystyle \mu _{1}(\Sigma _{11})^{-1}\Sigma _{12}=0} and Σ 21 ( Σ 11 ) −
Reasoning model
A reasoning model, also known as a reasoning language model (RLM) or large reasoning model (LRM), is a type of large language model (LLM) that has been specifically trained to solve complex tasks requiring multiple steps of logical reasoning. These models demonstrate superior performance on logic, mathematics, and programming tasks compared to standard LLMs. They possess the ability to revisit and revise earlier reasoning steps and utilize additional computation during inference as a method to scale performance, complementing traditional scaling approaches based on training data size, model parameters, and training compute. == Overview == Unlike traditional language models that generate responses immediately, reasoning models allocate additional compute, or thinking, time before producing an answer to solve multi-step problems. OpenAI introduced this terminology in September 2024 when it released the o1 series, describing the models as designed to "spend more time thinking" before responding. The company framed o1 as a reset in model naming that targets complex tasks in science, coding, and mathematics, and it contrasted o1's performance with GPT-4o on benchmarks such as AIME and Codeforces. Independent reporting the same week summarized the launch and highlighted OpenAI's claim that o1 automates chain-of-thought style reasoning to achieve large gains on difficult exams. In operation, reasoning models generate internal chains of intermediate steps, then select and refine a final answer. OpenAI reported that o1's accuracy improves as the model is given more reinforcement learning during training and more test-time compute at inference. The company initially chose to hide raw chains and instead return a model-written summary, stating that it "decided not to show" the underlying thoughts so researchers could monitor them without exposing unaligned content to end users. Commercial deployments document separate "reasoning tokens" that meter hidden thinking and a control for "reasoning effort" that tunes how much compute the model uses. These features make the models slower than ordinary chat systems while enabling stronger performance on difficult problems. == History == The research trajectory toward reasoning models combined advances in supervision, prompting, and search-style inference. Early alignment work on reinforcement learning from human feedback showed that models can be fine-tuned to follow instructions with "human feedback" and preference-based rewards. In 2022, Google Research scientists Jason Wei and Denny Zhou showed that chain-of-thought prompting "significantly improves the ability" of large models on complex reasoning tasks. Input → Step 1 → Step 2 → ⋯ → Step n ⏟ Reasoning chain → Answer {\displaystyle {\text{Input}}\rightarrow \underbrace {{\text{Step}}_{1}\rightarrow {\text{Step}}_{2}\rightarrow \cdots \rightarrow {\text{Step}}_{n}} _{\text{Reasoning chain}}\rightarrow {\text{Answer}}} A companion result demonstrated that the simple instruction "Let's think step by step" can elicit zero-shot reasoning. Follow-up work introduced self-consistency decoding, which "boosts the performance" of chain-of-thought by sampling diverse solution paths and choosing the consensus, and tool-augmented methods such as ReAct, a portmanteau of Reason and Act, that prompt models to "generate both reasoning traces" and actions. Research then generalized chain-of-thought into search over multiple candidate plans. The Tree-of-Thoughts framework from Princeton computer scientist Shunyu Yao proposes that models "perform deliberate decision making" by exploring and backtracking over a tree of intermediate thoughts. OpenAI's reported breakthrough focused on supervising reasoning processes rather than only outcomes, with Lightman et al.'s "Let's Verify Step by Step" reporting that rewarding each correct step "significantly outperforms outcome supervision" on challenging math problems and improves interpretability by aligning the chain-of-thought with human judgment. OpenAI's o1 announcement ties these strands together with a large-scale reinforcement learning algorithm that trains the model to refine its own chain of thought, and it reports that accuracy rises with more training compute and more time spent thinking at inference. Together, these developments define the core of reasoning models. They use supervision signals that evaluate the quality of intermediate steps, they exploit inference-time exploration such as consensus or tree search, and they expose controls for how much internal thinking compute to allocate. OpenAI's o1 family made this approach available at scale in September 2024 and popularized the label "reasoning model" for LLMs that deliberately think before they answer. The development of reasoning models illustrates Richard S. Sutton's "bitter lesson" that scaling compute typically outperforms methods based on human-designed insights. This principle was demonstrated by researchers at the Generative AI Research Lab (GAIR), who initially attempted to replicate o1's capabilities using sophisticated methods including tree search and reinforcement learning in late 2024. Their findings, published in the "o1 Replication Journey" series, revealed that knowledge distillation, a comparatively straightforward technique that trains a smaller model to mimic o1's outputs, produced unexpectedly strong performance. This outcome illustrated how direct scaling approaches can, at times, outperform more complex engineering solutions. === Drawbacks === Reasoning models require significantly more computational resources during inference compared to non-reasoning models. Research on the American Invitational Mathematics Examination (AIME) benchmark found that reasoning models were 10 to 74 times more expensive to operate than their non-reasoning counterparts. The extended inference time is attributed to the detailed, step-by-step reasoning outputs that these models generate, which are typically much longer than responses from standard large language models that provide direct answers without showing their reasoning process. One researcher in early 2025 argued that these models may face potential additional denial-of-service concerns with "overthinking attacks." === Releases === ==== 2024 ==== In September 2024, OpenAI released o1-preview, a large language model with enhanced reasoning capabilities. The full version, o1, was released in December 2024. OpenAI initially shared preliminary results on its successor model, o3, in December 2024, with the full o3 model becoming available in 2025. Alibaba released reasoning versions of its Qwen large language models in November 2024. In December 2024, the company introduced QvQ-72B-Preview, an experimental visual reasoning model. In December 2024, Google introduced Deep Research in Gemini, a feature designed to conduct multi-step research tasks. On December 16, 2024, researchers demonstrated that by scaling test-time compute, a relatively small Llama 3B model could outperform a much larger Llama 70B model on challenging reasoning tasks. This experiment suggested that improved inference strategies can unlock reasoning capabilities even in smaller models. ==== 2025 ==== In January 2025, DeepSeek released R1, a reasoning model that achieved performance comparable to OpenAI's o1 at significantly lower computational cost. The release demonstrated the effectiveness of Group Relative Policy Optimization (GRPO), a reinforcement learning technique used to train the model. On January 25, 2025, DeepSeek enhanced R1 with web search capabilities, allowing the model to retrieve information from the internet while performing reasoning tasks. Research during this period further validated the effectiveness of knowledge distillation for creating reasoning models. The s1-32B model achieved strong performance through budget forcing and scaling methods, reinforcing findings that simpler training approaches can be highly effective for reasoning capabilities. On February 2, 2025, OpenAI released Deep Research, a feature powered by their o3 model that enables users to conduct comprehensive research tasks. The system generates detailed reports by automatically gathering and synthesizing information from multiple web sources. OpenAI called GPT-4.5 its "last non-chain-of-thought model", and implemented with GPT-5 a router model that selects a model based on the difficulty of the task. ==== 2026 ==== In January 2026, Moonshot AI released Kimi K2.5, an open-source 1 trillion parameter MoE model with 32 billion active parameters. It uses an “Agent Swarm” system that dynamically decomposes tasks into sub-agents for reasoning and execution, enabling more scalable multi-step problem solving than a single sequential reasoning chain. == Training == Reasoning models follow the familiar large-scale pretraining used for frontier language models, then diverge in the post-training and optimization. OpenAI reports that o1 is trained with a large-
Jailbreak (computer science)
In computer security, jailbreaking is defined as the act of removing limitations that a vendor attempted to hard-code or hard-wire into its hardware and/or software. It is a form of privilege escalation. The term may have originated with the use of toolsets to break out of a chroot or jail in UNIX-like operating systems. This allowed the user to see files outside of the file system that the administrator intended to make available to the application or user in question. The term was first used in its modern meaning in the iPhone/iOS jailbreaking community and has also been used as a term for PlayStation Portable hacking; these devices have repeatedly been subject to jailbreaks, allowing the execution of arbitrary code, and sometimes have had those jailbreaks disabled by vendor updates, especially in the case of iOS devices. == iOS jailbreaking == iOS systems including the iPhone, iPad, and iPod Touch have been subject to iOS jailbreaking efforts since they were released, and continuing with each firmware update. iOS jailbreaking tools have included the option to install package frontends such as Cydia and Installer.app, third-party alternatives to the App Store, as a way to find and install system tweaks and binaries. To prevent iOS jailbreaking, Apple has made the device boot ROM execute checks for SHSH blobs in order to disallow uploads of custom kernels and prevent software downgrades to earlier, jailbreakable firmware. In an "untethered" jailbreak, the iBoot environment is changed to execute a boot ROM exploit and allow submission of a patched low level bootloader or hack the kernel to submit the jailbroken kernel after the SHSH check. == Other phones == A similar method of jailbreaking exists for S60 Platform smartphones, where utilities such as HelloOX allow the execution of unsigned code and full access to system files. or edited firmware (similar to the M33 hacked firmware used for the PlayStation Portable) to circumvent restrictions on unsigned code. Nokia has since issued updates to curb unauthorized jailbreaking, in a manner similar to Apple. Rooting is the equivalent concept for Android phones and other devices. == Console jailbreaking == In the case of gaming consoles, jailbreaking is often used to execute homebrew games. In 2011, Sony, with assistance from law firm Kilpatrick Stockton, sued 21-year-old George Hotz and associates of the group fail0verflow for jailbreaking the PlayStation 3 (see Sony Computer Entertainment America v. George Hotz and PlayStation Jailbreak). == AI jailbreaks == Jailbreaking can also occur in systems and software that use generative artificial intelligence models, such as ChatGPT. In jailbreaking attacks on artificial intelligence systems, users are able to manipulate the system to behave differently than it was intended, making it possible to reveal information about how the model was instructed by the vendor (the "system prompt") or to induce it to respond in an anomalous or harmful way. These attacks typically simply require prompting the AIs with specific phrasal templates - no software is typically required, although software could theoretically be used to "industrialise" such exploits, and some research has been done in this direction. In 2024, a consortium of AI firms founded HackAPrompt.com, a competition to encourage users to find new and effective AI jailbreaking techniques. These and other findings from "ethical hackers" have been used by AI model providers to try to improve AI safety.